Abstract

An efficient optimization strategy for the design of diffractive optical elements that is based on rigorous diffraction theory is described. The optimization algorithm combines diffraction models of different degrees of accuracy and computational complexity. A fast design algorithm for diffractive optical elements is used to yield estimates of the optimum surface profile based on paraxial diffraction theory. These estimates are subsequently evaluated with a rigorous diffraction model. This scheme allows one to minimize the need to compute diffraction effects rigorously, while providing accurate design. We discuss potential applications of this scheme as well as details of an implementation based on a modified Gerchberg–Saxton algorithm and the finite-difference time-domain method. Illustrative examples are provided in which we use the algorithm to design Fourier array illuminators.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. J. N. Mait, D. W. Prather, M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zero-order effective-medium theory,” J. Opt. Soc. Am. A 16, 1157–1167 (1999).
    [CrossRef]

2000

1999

1995

1994

1990

F. C. Lin, M. A. Fiddy, “Image estimation from scattered filed data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

1980

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Commun. 19, 297–305 (1980).

Arrizon, V.

Bräuer, R.

R. Bräuer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in non-paraxial region,” Opt. Commun. 115, 411–416 (1995).
[CrossRef]

Brenner, K.-H.

Bryngdahl, O.

R. Bräuer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in non-paraxial region,” Opt. Commun. 115, 411–416 (1995).
[CrossRef]

Chen, Y.

Doskolovich, L.

V. Soifer, V. Kotlyar, L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, London, 1997).

Fiddy, M. A.

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

F. C. Lin, M. A. Fiddy, “Image estimation from scattered filed data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Commun. 19, 297–305 (1980).

Grann, E. B.

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics, the Finite Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass.2000).

Herzig, H.-P.

H.-P. Herzig, “Design of diffractive and refractive micro-optics,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 1–29.

Jahns, J.

Jiang, J.

J. Jiang, G. P. Nordin, “A rigorous unidirectional method for designing finite aperture diffractive optical elements,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington D.C., 2000), pp. 13–15.

Judkins, J. B.

Kotlyar, V.

V. Soifer, V. Kotlyar, L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, London, 1997).

Lin, F. C.

F. C. Lin, M. A. Fiddy, “Image estimation from scattered filed data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

Mait, J. N.

Mirotznik, M. S.

Moharam, M. G.

Noponen, E.

Nordin, G. P.

J. Jiang, G. P. Nordin, “A rigorous unidirectional method for designing finite aperture diffractive optical elements,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington D.C., 2000), pp. 13–15.

Pommet, D. A.

Prather, D. W.

J. N. Mait, D. W. Prather, M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zero-order effective-medium theory,” J. Opt. Soc. Am. A 16, 1157–1167 (1999).
[CrossRef]

D. W. Prather, S. Shi, “Hybrid scalar-vector method for the analysis of electrically large finite aperiodic diffractive optical elements,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators IV, I. Cindrich, S. H. Lee, R. L. Sutherland, Proc. SPIE3633, 2–13 (1999).
[CrossRef]

Shi, S.

D. W. Prather, S. Shi, “Hybrid scalar-vector method for the analysis of electrically large finite aperiodic diffractive optical elements,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators IV, I. Cindrich, S. H. Lee, R. L. Sutherland, Proc. SPIE3633, 2–13 (1999).
[CrossRef]

Singer, W.

Sinzinger, S.

Soifer, V.

V. Soifer, V. Kotlyar, L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, London, 1997).

Song, H.

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics, the Finite Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass.2000).

Testorf, M.

Testorf, M. E.

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

Turunen, J.

E. Noponen, J. Turunen, F. Wyrowski, “Synthesis of paraxial-domain diffractive optical elements by rigorous electromagnetic theory,” J. Opt. Soc. Am. A 12, 1128–1133 (1995).
[CrossRef]

J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 31–52 and references therein.

Wang, Z.

Wyrowski, F.

Yatagai, T.

Yoshikawa, N.

Zhou, G.

Ziolkowski, R. W.

Appl. Opt.

Int. J. Imaging Syst. Technol.

F. C. Lin, M. A. Fiddy, “Image estimation from scattered filed data,” Int. J. Imaging Syst. Technol. 2, 76–95 (1990).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Commun. 19, 297–305 (1980).

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

R. Bräuer, O. Bryngdahl, “Design strategy of diffractive elements with prescribed diffraction angles in non-paraxial region,” Opt. Commun. 115, 411–416 (1995).
[CrossRef]

Other

J. Jiang, G. P. Nordin, “A rigorous unidirectional method for designing finite aperture diffractive optical elements,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington D.C., 2000), pp. 13–15.

D. W. Prather, S. Shi, “Hybrid scalar-vector method for the analysis of electrically large finite aperiodic diffractive optical elements,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators IV, I. Cindrich, S. H. Lee, R. L. Sutherland, Proc. SPIE3633, 2–13 (1999).
[CrossRef]

J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 31–52 and references therein.

V. Soifer, V. Kotlyar, L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, London, 1997).

H.-P. Herzig, “Design of diffractive and refractive micro-optics,” in Micro-Optics, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 1–29.

A. Taflove, S. C. Hagness, Computational Electrodynamics, the Finite Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass.2000).

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Figures (6)

Fig. 1
Fig. 1

Schematic of rigorous optimization of diffractive optical elements.

Fig. 2
Fig. 2

Design of a 1:17 Fourier beam splitter with a grating period d=64λ: (a) paraxial design, (b) response after one cycle of the optimization algorithm, (c) response after six cycles.

Fig. 3
Fig. 3

Design of a 1:17 Fourier beam splitter whose surface profile is calculated from the unwrapped phase distribution: (a) response after one cycle of the optimization algorithm, (b) response after five cycles.

Fig. 4
Fig. 4

Design of a 1:9 Fourier beam splitter. Response after seven cycles of the optimization algorithm.

Fig. 5
Fig. 5

Surface profiles of optimum designs: (a) surface profile of the Fourier beam splitter in Fig. 3(b), (b) difference between surface profiles of the rigorous and the paraxial designs, (c) surface profile for the beam splitter in Fig. 4, (d) difference between rigorous and paraxial designs.

Fig. 6
Fig. 6

Design of a 1:9 Fourier beam splitter with a grating period d=16λ. Result after 13 optimization cycles: (a) far-field intensity, (b) difference between surface profiles of the rigorous and the paraxial designs.

Equations (2)

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sin α=m(λ/d),
ϕ(x)=-2 2πλh(x)cos α,

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